Multihump fundamental solitons in the multi-component Mel’nikov system

Abstract

In this paper, the multihump fundamental $N$-soliton solution for the multi-component Mel’nikov system is derived by combining the Hirota bilinear method with the variable separation approach. In this solution, each short-wave component contains $N$ arbitrary functions of the variable $y$. By assigning different functional forms to these arbitrary functions, various types of multihump soliton solutions, including chaotic, fractal, and folded solitons, can be generated, thereby significantly enhancing the diversity of multihump solitons. Furthermore, the study demonstrates that for the arbitrary functions in the same component of the multihump multi-soliton solution, selecting different functional forms leads to hybrid solutions with solitons of different waveforms, such as dromion-like solitons appearing alongside linear solitons, and curved solitons coexisting with serpentine solitons. This finding provides an effective approach for exploring the interaction dynamics among different types of multihump solitons in nonlinear physics.